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UBC Theses and Dissertations

Study of ferroresonance with application to digital logic Reed, Albert James


A series resonant L-C circuit in which either the inductor or the capacitor is nonlinear and which is excited by a sinusoidal voltage of a fixed frequency may have two steady-state responses. One of these responses is characterized by a high amplitude oscillation; the other by a low one. If the amplitude or frequency of the driving signal is varied slowly, the response may suddenly change or "jump" to the other state. As a result, this phenomenon has been called jump resonance, or ferroresonance. Because the high and low resonant states could be considered as a 0 and 1 basis for digital logic operations, it was the purpose of this work to study the phenomenon and to investigate the possibility of using it in the design of digital logic elements. Equations which exhibit the necessary features were studied on an analogue computer. The results of the study were used as design criteria for the construction of an actual circuit and also as a basis for an approximate analytical study. The analytical study uses the Ritz method to find useful features of the responses. The results of previous users of this method have been extended to include equations with both second derivative coupling and non-symmetrical non-linearities. Based on the above studies, a prototype circuit was designed which has some of the basic properties of conventional flip-flop circuits. One of the main features of this circuit is that it is almost entirely made of reactive components and as a result has very low power consumption. The operation of the circuit is used to verify the validity of the approximations made in both the analogue simulation and the analytical study. The results obtained from the analogue study, the Ritz analysis, and the prototype circuit compare favorably with each other. Some suggestions for future work are given.

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